To evaluate the linear function $g(x) = 3x - 5$ for specific algebraic expressions, substitute each expression for the independent variable $x$ and simplify using the order of operations:

• Evaluate $g(h^2)$: Replace $x$ with $h^2$ to get $g(h^2) = 3(h^2) - 5$. Simplify to yield $g(h^2) = 3h^2 - 5$.
• Evaluate $g(x+2)$: Replace $x$ with the binomial $(x+2)$ using parentheses to get $g(x+2) = 3(x+2) - 5$. Distribute the $3$ to obtain $3x + 6 - 5$. Simplify by combining the constant terms to find $g(x+2) = 3x + 1$.
• Evaluate $g(x) + g(2)$: This expression requires finding the value of $g(2)$ first and adding it to the expression for $g(x)$. Find $g(2) = 3(2) - 5 = 6 - 5 = 1$. Then, substitute both parts into the sum to get $g(x) + g(2) = (3x - 5) + (1)$. Simplify by combining the constant terms to find $g(x) + g(2) = 3x - 4$.

Notice that evaluating a sum, such as $g(x+2)$, is not necessarily equal to the sum of the evaluated function values, $g(x) + g(2)$.